Photochemical reactions on the surface of a circular disk: A theoretical approach to kinetics in restricted two-dimensional space

Kinetics of decay of excited donor molecules B* by static and diffusion-induced electron and energy transfer to accepters (A) in restricted two-dimensional space, as described by the surface of a circular disk (circle), have been examined. In the first instance, an analytical solution is given to outline the decay of B* by a static distance-dependent electron and energy transfer process to some random accepters. Results show that luminescence decay of B* on a restricted two-dimensional surface is slower than a similar decay on an infinite surface, with the difference between the kinetics in restricted space and infinite space increasing with increasing observation time. The decay of B* molecules on diffusion approach of reagents along the two-dimensional disk surface is exponential at sufficiently long times, a kinetic behavior that contrasts with the long-time behavior of diffusion-limited decay processes taking place on an infinite surface where the rate constant does not achieve an asymptotic value even for long times, Decay processes of excited triplet molecules of B* by triplet-triplet (T-T) annihilation on the restricted circle were also examined. These differ principally from those of luminescence quenching by the fact that the concentrations of surface-reacting species are equal. An approximate solution to T-T annihilation by static interactions is described on the basis of the average reagent concentration approximation and with the assumption that, in the course of the annihilation process, the triplet molecules are always randomly distributed at the prevalent mean surface concentration. The decay kinetics described by the analytical expressions derived agree fairly well with the results from Monte Carlo simulations. Kinetic expressions for diffusion-induced annihilation on the two-dimensional restricted surface are also described using an infinite space approximation for the rate constant; Monte Carlo simulations indicate that the resulting kinetic solution is useful to analyse the decay process on the circular disk provided that the effective radius of the annihilation event does not exceed one tenth the disk radius.